Question

greek architects considered a rectangle whose length was approximately 1.6 times its width to be the most visually appealing. write an equation for the length and width of a rectangle constructed in this manner if the sum of the length and width is 156 ft. (let w represent the width of the rectangle.) find the length and width of a rectangle. length ft width ft

Explanation:

Step1: Write the equation

Let \( W \) be the width. The length \( L = 1.6W \). The sum of length and width is \( L+W=156 \). Substitute \( L = 1.6W \) into the sum - equation: \( 1.6W+W = 156 \).

Step2: Simplify the left - hand side of the equation

Combine like terms: \( (1.6 + 1)W=156 \), so \( 2.6W = 156 \).

Step3: Solve for \( W \)

Divide both sides of the equation by \( 2.6 \): \( W=\frac{156}{2.6}=60 \).

Step4: Solve for \( L \)

Since \( L = 1.6W \), substitute \( W = 60 \) into the formula: \( L=1.6\times60 = 96 \).

Answer:

The width \( W = 60\) ft and the length \( L = 96\) ft.